Footnote marks at end of a sentence

Both are valid ways to place a footnote reference, but they mean slightly different things.

If you want the footnote reference to belong to the entire sentence, then the second method is correct. However, if you want the footnote to apply only to the word text, then the first is correct.

Noldorin and SabreWolfy have logical answers, but in the world of typesetting, logic is not respected. At least in the field of scientific publishing, where footnotes and references are common, publishers tend to have very strict guidelines about where they want the marks. In that case, you're not really free to choose yourself. For example, most of the physics and chemistry journals want references after punctuation:

as first demonstrated by Smith.¹

As a consequence, in these fields, people mostly tend to follow this usage, even in works for which there is no restriction imposed.

So, what I'm saying is: if you're free to do what you want, go ahead, but check the relevant style guide first.

My understanding is that if the footnote refers only to the word text then it should be placed immediately after the word, as in the first case above. If the footnote refers to the entire sentence (or at least to the last phrase, for example), then it should be placed after the stop.